Simplify fourth root of 256x^6* square root of 100x^9

$\sqrt[4]{256 x^{6}} \cdot \sqrt{100 x^{9}}$

Step 1

Rewrite $256 x^{6}$ as ${(4 x)}^{4} x^{2}$ .

Rewrite $256$ as $4^{4}$ .

$\sqrt[4]{4^{4} x^{6}} \cdot \sqrt{100 x^{9}}$

Factor out $x^{4}$ .

$\sqrt[4]{4^{4} (x^{4} x^{2})} \cdot \sqrt{100 x^{9}}$

Rewrite $4^{4} x^{4}$ as ${(4 x)}^{4}$ .

$\sqrt[4]{{(4 x)}^{4} x^{2}} \cdot \sqrt{100 x^{9}}$

Step 2

Pull terms out from under the radical.

$4 x \sqrt[4]{x^{2}} \cdot \sqrt{100 x^{9}}$

Step 3

Rewrite $\sqrt[4]{x^{2}}$ as $\sqrt{\sqrt{x^{2}}}$ .

$4 x \sqrt{\sqrt{x^{2}}} \cdot \sqrt{100 x^{9}}$

Step 4

Pull terms out from under the radical, assuming positive real numbers.

$4 x \sqrt{x} \cdot \sqrt{100 x^{9}}$

Step 5

Rewrite $100 x^{9}$ as ${(10 x^{4})}^{2} x$ .

Rewrite $100$ as $10^{2}$ .

$4 x \sqrt{x} \cdot \sqrt{10^{2} x^{9}}$

Factor out $x^{8}$ .

$4 x \sqrt{x} \cdot \sqrt{10^{2} (x^{8} x)}$

Rewrite $x^{8}$ as ${(x^{4})}^{2}$ .

$4 x \sqrt{x} \cdot \sqrt{10^{2} ({(x^{4})}^{2} x)}$

Rewrite $10^{2} {(x^{4})}^{2}$ as ${(10 x^{4})}^{2}$ .

$4 x \sqrt{x} \cdot \sqrt{{(10 x^{4})}^{2} x}$

Step 6

Pull terms out from under the radical.

$4 x \sqrt{x} \cdot (10 x^{4} \sqrt{x})$

Step 7

Multiply $x$ by $x^{4}$ by adding the exponents.

Move $x^{4}$ .

$4 (x^{4} x) \sqrt{x} \cdot (10 \sqrt{x})$

Multiply $x^{4}$ by $x$ .

Raise $x$ to the power of $1$ .

$4 (x^{4} x^{1}) \sqrt{x} \cdot (10 \sqrt{x})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$4 x^{4 + 1} \sqrt{x} \cdot (10 \sqrt{x})$

Add $4$ and $1$ .

$4 x^{5} \sqrt{x} \cdot (10 \sqrt{x})$

Step 8

Multiply $4 x^{5} \sqrt{x} (10 \sqrt{x})$ .

Multiply $10$ by $4$ .

$40 x^{5} \sqrt{x} \sqrt{x}$

Raise $\sqrt{x}$ to the power of $1$ .

$40 x^{5} ({\sqrt{x}}^{1} \sqrt{x})$

Raise $\sqrt{x}$ to the power of $1$ .

$40 x^{5} ({\sqrt{x}}^{1} {\sqrt{x}}^{1})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$40 x^{5} {\sqrt{x}}^{1 + 1}$

Add $1$ and $1$ .

$40 x^{5} {\sqrt{x}}^{2}$

Step 9

Rewrite ${\sqrt{x}}^{2}$ as $x$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x}$ as $x^{\frac{1}{2}}$ .

$40 x^{5} {(x^{\frac{1}{2}})}^{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$40 x^{5} x^{\frac{1}{2} \cdot 2}$

Combine $\frac{1}{2}$ and $2$ .

$40 x^{5} x^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$40 x^{5} x^{\frac{2}{2}}$

Rewrite the expression.

$40 x^{5} x^{1}$

Simplify.

$40 x^{5} x$

Step 10

Multiply $x^{5}$ by $x$ by adding the exponents.

Move $x$ .

$40 (x \cdot x^{5})$

Multiply $x$ by $x^{5}$ .

Raise $x$ to the power of $1$ .

$40 (x^{1} x^{5})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$40 x^{1 + 5}$

Add $1$ and $5$ .

$40 x^{6}$

Simplify fourth root of 256x^6* square root of 100x^9

Related Questions

Support LCMGCF.com by disabling your adblocker.